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<article class="li"><h3 class="heading">
<span class="type">Item</span><span class="period">.</span>
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<p>If <span class="process-math">\(\displaystyle\sum_{n=0}^{\infty} a_n(x-x_0)^n=\sum_{n=0}^{\infty} b_n(x-x_0)^n\)</span> for all <span class="process-math">\(x\)</span> in the interval of convergence, then</p>
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\begin{equation*}
\textcolor{magenta}{a_n=b_n\quad \text{ for all } n}.
\end{equation*}
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<p>Namely, if two power series are <dfn class="terminology">equal</dfn>, then they must have the same coefficients.</p></article><span class="incontext"><a href="sec5_1.html#li-15" class="internal">in-context</a></span>
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